We have 9 years process model which has few instances running currently on production. In which they have assigned tasks to one particular user who had left the organization now. How we can handle this one?
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That is a business decision. I suggest to assign the tasks to another person.
I'd also encourage you to design into the process model an escalation path so that future tasks are not stranded in a similar way. Something like waiting for a period of time (e.g. 5 days), sending the assignee a reminder, then waiting 2 more days and then re-assigning to a manager's group - whatever makes sense for the organization that this is being used in.
Escalation & exception won't work if the node is failing.Also those current instances are on production so we cannot manually edit those instances
You didn't mention that the nodes had failed.
Even if they had failed then, yes, you can manually edit a running instance in order to fix it.
I was also advocating you evolve the design of the process model in Dev, test the scenarios where you want to implement escalations, and then push those into Production so that future instances do not encounter the same problems. This is how any application is improved over time.
We have process instances are more in number. How can we manually edit, so it will take too much of time. Do we have another possible way?
Ok, so by "few" you meant "many"...
There's this: https://community.appian.com/b/appmarket/posts/task-management-smart-services
That would help with bulk reassignment. As for handling nodes that are currently in error...it doesn't help you, but you should have a support regime in place that addresses any Production errors as soon as they occur so you don't end up with a backlog of in-error process instances.